Thursday, September 3, 2009

EMH and the role of arbitrageurs

The Efficient Market Hypothesis (EMH) has borne the brunt of the attacks against modern financial engineering and theories in the aftermath of the bursting of the sub-prime mortgage bubble. The EMH had argued that prices of all traded financial assets reflect all known information and any new random information is immediately traded into the price of the asset or any deviation from the true value (by a noise trader) of the security is swiftly traded away. This also has been taken to mean that nobody can predict the market and thereby beat it on a sustained basis. Now here comes more "stakes through the heart of EMH".

In a superb post at Baseline Scenario, Mike Konczal points to a classic 1997 paper by Andrei Shleifer and Robert Vishny, The Limits of Arbitrage, which illustrated the difference between the conventional models of arbitrage, which required no capital and entailed no risk, with the real world where both assumptions fail. They argue that professional arbitrage, typically done by traders with other people's capital, "becomes ineffective (in bringing security prices to their fundamental values) in certain circumstances, when prices diverge far from fundamental values". Such extreme circumstances and the associated volatility exposes arbitrageurs to "risks of losses and the need to liquidate the portfolio under pressure from investors in the fund". Konczal refers to the role of arbitrageurs thus,

"(Arbitrageurs) will take prices that are out of line and bring them back into line, making a good fee and making prices reflect all available information, the very building block necessary for EMH to work... (They) can’t do their job if they are time or credit constrained. Specifically, if they are highly leveraged, and prices move against their position before they return to their fundamental value – if the market stays irrational longer than they can remain solvent – they’ll collapse before they can do their job."

In other words, under certain cirumstances, markets may deviate from the true value and the arbitrageurs may fail to price in or trade away the deviation, thereby negating the EMH. In these circumstances, traders face actual constraints over scarce resources such as time and capital and fail to get to the other side of the trade.

Arbitrage is defined as the "simultaneous purchase and sale of the same, or essentially similar, security in two different markets for advantageously different prices". Arbitrageurs perform the important role of aligning prices across all markets, in accordance with the "law of one price" and thereby keeping the markets efficient. Accordingly, in their absence, prices can stray away from their true values, leaving the market vulnerable to manipulation and bubbles.

Konczal argues that bond and forex markets, where it is either easier to calculate valuations or to go after Central Bankers attempting to maintain non-market exchange rates, attracts arbitrageurs. In contrast, stock markets - with their difficulty of valuations and long delays in realizing gains - and housing markets with the lack of instrumenbts to directly hold postions in the housing market, are not very attractive for arbitrageurs. This post-facto rationalization sits in well with the relative volatility levels across these markets in the build-up and aftermath of the sub-prime bubble.

About the claim that nobody can systematically beat the stock market, implying nobody can predict a market crash, Richard Serlin writes,

"For EMH to be wrong, or very far from the truth, all you have to show is that you can predict with just a substantial degree of accuracy. So, if you can just show, for example, that the odds of a stock market crash are far higher in years when the P-E ratio is much higher than average (or for housing crashes the buy-rent, or price-household income ratio), or that the expected risk-adjusted long run return is much lower than average, or other “anomalies” (anomalous to the EMH) like this, then you can show that the EMH is substantially far from the truth."

And about the strong possibility of deviations from true value persisting and staying beyond the reach of arbitrageurs,

"A smart rational investor is limited in how much of a mispriced stock he will purchase or sell by how undiversified his portfolio will become. For example, suppose IBM is currently selling for $100, but its efficient, or rational informed, price is $110. It must be remembered that the rational informed price is what the stock is worth to the investor when added in the appropriate proportion to his properly diversified portfolio of other assets. Such a savvy investor will purchase more IBM as it only costs $100, but as soon as he purchases more IBM, IBM becomes worth less to him per share, because it becomes increasingly risky to put so much of his money in the IBM basket. By the time this investor has purchased enough IBM that it constitutes 20 percent of his portfolio, the stock may have become so risky that it’s worth less than $100 to him for an additional share. At that point he may have only purchased enough IBM stock to push the price to $100.02, far short of its efficient market price of $110. Thus, if the rational and informed investors do not hold or control enough—a large enough proportion of the wealth invested in the market—they may not be able to come close to pushing prices to the efficient level."

Update 1 (10/4/2010)Denis Gromb and Dimitri Vayanos review the "limits to arbitrage" – whereby arbitrageurs cannot always raise the capital they need - and argues that regulation incentivising or even forcing arbitrageurs to take less risk could make everyone better off, arbitrageurs included. However, as they write, there is no unanimity on what is the best approach to achieve this - risk-based capital requirements or taxes and subsidies or a lender of last resort policy or asset purchase programs or something else?